Edge-based graph neural network for ranking critical road segments in a network

Transportation networks play a crucial role in society by enabling the smooth movement of people and goods during regular times and acting as arteries for evacuations during catastrophes and natural disasters. Identifying the critical road segments in a large and complex network is essential for planners and emergency managers to enhance the network’s efficiency, robustness, and resilience to such stressors. We propose a novel approach to rapidly identify critical and vital network components (road segments in a transportation network) for resilience improvement or post-disaster recovery. We pose the transportation network as a graph with roads as edges and intersections as nodes and deploy a Graph Neural Network (GNN) trained on a broad range of network parameter changes and disruption events to rank the importance of road segments. The trained GNN model can rapidly estimate the criticality rank of individual road segments in the modified network resulting from an interruption. We address two main limitations in the existing literature that can arise in capital planning or during emergencies: ranking a complete network after changes to components and addressing situations in post-disaster recovery sequencing where some critical segments cannot be recovered. Importantly, our approach overcomes the computational overhead associated with the repeated calculation of network performance metrics, which can limit its use in large networks. To highlight scenarios where our method can prove beneficial, we present examples of synthetic graphs and two real-world transportation networks. Through these examples, we show how our method can support planners and emergency managers in undertaking rapid decisions for planning infrastructure hardening measures in large networks or during emergencies, which otherwise would require repeated ranking calculations for the entire network.

The research award (Award No. 20220480) was received by SN and ET from the funding agency Los Angeles Bureau of Engineering (https://engineering.lacity.gov/).The funders had no role in study design, data collection, and analysis, the decision to publish, or preparation of the manuscript.
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We have deleted the funding information-related statement from the Acknowledgements, have modified the funding statement, and included it in the cover letter.
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Response to Comments from Reviewer #1
Reviewer: This paper studies the task of ranking critical road segments for transportation networks.The authors pose the transportation network as a graph with roads as edges and intersections as nodes and deploy a Graph Neural Network (GNN) for the task.
Strength: 1. Ranking critical road segments is indeed a challenging and meaningful task for transportation networks.GNNs are suitable approaches for the task.
2. The idea of the paper is reasonable and easy to follow.
3. The paper presents the result on both synthetic and real-world graph data, experimental settings (i.e., hyper-parameters and complexity analysis) are provided.
4. Some applications of the proposed framework are presented.
Response: We thank the reviewer for their positive assessment, insightful comments, and constructive feedback.We have diligently addressed all of the questions and have provided our responses below.
Reviewer: Questions: 1.The paper generates 1000 training graphs, 100 validation graphs, and 100 test graphs.What's the difference with a single real-world road network (i.e., U.S. Freeway network), what are the train, valid and test dataset details of the real-world network?
Response: In our real-world network scenario, we generate training, testing, and validation datasets by modifying edge weights between nodes, following Case I and Case II protocols.These edge weights correspond to travel times obtained from the Google distance matrix API [4].Minor congestion affects travel times, resulting in varying edge weights for each dataset.In Case I, we adjust only the edge weights, while in Case II, we modify both the number of edges and their weights within the graph.We have revised the following text as follows.
This following ablation study simulates the edge importance ranking due to a dynamic change in the network parameters resulting from construction activities or functional factors such as travel time.Two scenarios are considered in this study: (i) Case I: In this case, the effects of minor congestion or interruption of traffic on roads are simulated through random perturbations in the edge weights according to r × Ω i where Ω i is the weight of edge i, and the values of r are sampled from a uniform distribution The number of nodes and edges for the graphs remains unchanged.
(ii) Case II: In this case, major interruption scenarios rendering a small number of edges inoperable, such as from accidents or natural disasters, are simulated.In addition to the edge weights specified previously, i.e., r × Ω i with r ∈ U [0.8, 1.2], the number of edges in the graph is modified as well.The number of edges is sampled from a discrete uniform distribution ⌊U [0.99, 1] × E ⌉ -which is based on a maximum of 1% edge deletion from the original network.Here, ⌊•⌉ denotes the nearest integer function.While the 1% edge deletion number is arbitrarily assumed for the ablation study, this is not far from reports from previous events such as from a 20-year return period event resulting in 0.6%-0.7%loss in the road inventory [5].
We have also added the following sentence and the table caption to the revised manuscript for clarity.
In the context of GNN training, validation, and testing, the primary distinction among simulations lies in the change of edge weights, reflecting changes in travel time due to factors such as congestion (Case-I) and a deletion of edges (e.g., due to road closures) resulting from catastrophic events (Case-II).More details regarding this change can be found in Table 4. Table 4: Generation parameters of the transportation networks; for each network, the training, testing, and validation data are generated from a range of edge weights as follows: 8, for undirected graphs, and Response: We agree, the details are now contained in two tables, Table 2 and Table 4. Reviewer: 2.More experiments are needed like representation visualization to prove the effectiveness of the proposed framework.

Response:
We have now added experiments on four new transportation networks: Aachen city transportation network (Germany), Edinburgh city transportation network (Scotland), Road network of country of Luxembourg (Europe), and Santa Barbara city transportation network (US).The details about these networks are shown in Table 4.We have included these results in the revised manuscript.The Spearman's coefficient of our GNN-based framework on additional four worldwide networks are shown in Table 7.The average Spearman correlation exceeds 0.9, which underscores the performance of our approach.Response: We thank the reviewer for this comment.We will answer this in two parts as follows: Regarding citing the reviewer recommended papers: We thank the reviewer for suggesting the list of papers.We have included Zhao et al. [6] as it uses GNN for traffic forecasting which is relevant to the transportation network application.We have also included Ju el al. [7] as it provides a detailed literature review on graph representation learning.
However, we find that the remaining papers are not directly relevant to this work as they address a bus network [8], recommendation system [9,10], content-specific citation generation [11], clickthrough rate prediction [12], and capturing the evolving nature of user behaviors [13].
We have added the following sentences related to the works of Zhao et al. [6] and Ju el al. [7] in the revised paper.Such learning-based methods have been used in transportation networks for travel time prediction [14], traffic forecasting [6], and missing traffic data imputation [15].
GNN is a deep learning architecture that leverages the graph structure and feature information to perform various tasks, including node/edge/graph classification [16,7].
Regarding comparing SOTA baselines: The SOTA baseline methods can be categorized into two main groups: (a) utilitarian, which prioritizes overall efficiency or utility, and (b) egalitarian, which takes into account equity and population data while optimizing for efficiency.The utilitarian approach primarily relies on the topology of the transportation network, whereas the egalitarian approach incorporates both the origin-destination demand data and the network topology.In this paper, we have conducted a comparative analysis between our Graph Neural Network (GNN) based approach and several utilitarian methods, including (1) Edge betweenness Centrality, (2) Network efficiency-based vulnerability measure, and (3) Probabilistic measure of distance between networks.Based on computational efficiency, our GNN-based approach outperforms all the stateof-the-art methods.As part of our future work, we intend to integrate origin-destination demand data and equity-related information to compare our GNN based approach with egalitarian methods.Furthermore, it is worth noting that, to the best of our knowledge, while deep learning-based algorithms exist for approximating node importance ranking, there is currently no deep learningbased algorithm available for ranking the importance of edges or roads within the transportation network.This research endeavor was undertaken to address this gap.To address this in the revised manuscript, we have added the following sentences into the Conclusion section.
Additionally as a scope of future work, we intend to also integrate origin-destination demand data and equity-related information to compare our GNN based approach with egalitarian methods.

Response:
In response to the reviewer's comment, we have now added a new figure to aid in visual presentation.We have made the necessary changes in the manuscript text to reflect this.

Figure 15 :
Figure 15: Comparison between EBC based road ranking and the proposed GNN-based road ranking of US highway network for different scenarios; the color bar shows the road ranking.
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